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In this lesson, we will learn how to find the sum of a finite arithmetic series or the nth partial sum of an infinite arithmetic series to a particular term.

Q1:

Find the sum of the arithmetic series 3 + 6 + 9 + + 3 3 .

Q2:

Find the sum of the arithmetic series 6 + 9 + 1 2 + + 3 6 .

Q3:

Find the sum of the arithmetic series 1 3 + 1 9 + 2 5 + + 8 5 .

Q4:

Find the sum of the first 17 terms of the arithmetic series 1 2 + 2 1 + 3 0 + ⋯ .

Q5:

Find the sum of the first 18 terms of the arithmetic series 8 + 1 0 + 1 2 + ⋯ .

Q6:

Find the sum of the first 26 terms of the arithmetic series 7 + 8 + 9 + ⋯ .

Q7:

Find the sum of the arithmetic series √ 2 − √ 2 − 3 √ 2 − ⋯ − 9 √ 2 .

Q8:

Find the sum of the arithmetic series √ 5 − √ 5 − 3 √ 5 − ⋯ − 3 9 √ 5 .

Q9:

Samar devised a week-long study plan to prepare for finals. On the first day, she plans to study for 1 hour, and she will increase her study time by 30 minutes each successive day. How many total hours will Samar have spent studying at the end of the week?

Q10:

Find the sum of the integers between 4 and 57 that are divisible by 5.

Q11:

A fast food restaurant offers to give away two £100-prizes on one day. They will give away four £100-prizes the next day, six £100-prizes the next day, and so on, giving away two more £100-prizes each day than the previous day. If 𝑛 represents the number of days in their campaign, find a formula to calculate how many pounds they will they have given away in total by the end of the campaign.

Q12:

A boulder rolled down a mountain, gaining speed. It traveled 6 feet in the first second, and, in each successive second, it traveled 8 feet more than the previous second. How far did the boulder travel after 10 seconds?

Q13:

On New Year’s Eve, Sherif decided he wanted to do a lot more exercise. On the 1st of January, he would do one press-up. On the 2nd of January, he would do two press-ups. On the 3rd of January, he would do three press-ups and then he would carry on adding an extra press-up each day for a whole year. Assuming that he kept to his plan and that the next year was not a leap year, how many press-ups did he do throughout the entire year?

Q14:

Find the largest sum of the arithmetic sequence 1 1 7 , 1 0 9 , 1 0 1 , … .

Q15:

Find the largest sum of the arithmetic sequence 1 1 5 , 1 0 7 , 9 9 , … .

Q16:

Find the largest sum of the arithmetic sequence 1 1 7 , 1 0 1 , 8 5 , … .

Q17:

Using that 𝑆 𝑛 is the sum of the first 𝑛 terms of an arithmetic sequence with 𝑛 t h term 𝑇 𝑛 , decide if the following statement is correct:

To find the greatest sum of terms of an arithmetic sequence, we first find the number of positive terms by finding the largest integer 𝑚 for which 𝑇 > 0 𝑚 , and then calculate 𝑆 𝑚 which is the greatest sum.

Q18:

A fast food restaurant offers to give away two £ 1 0 0 prizes on June 1st. They will give away four £ 1 0 0 prizes on June 2nd, six £ 1 0 0 prizes on June 3rd, and so on, giving away two more £ 1 0 0 prizes each day than the previous day. How much money will they have given away in total by the end of June?

Q19:

Find the value of the series 3 1 1 5 − 1 1 5 + 3 2 1 5 − 2 1 5 + ⋯ + 5 9 1 5 − 2 9 1 5 + 6 0 1 5 − 3 0 1 5 .

Q20:

Find an expression for the sum of an arithmetic sequence whose first term is 𝑎 and whose common difference is 𝑑 .

Q21:

Find the sum of the second half of terms of the sequence ( 6 2 , 7 0 , 7 8 , , 1 5 0 ) .

Q22:

Find the sum of the second half of terms of the sequence ( − 5 5 , − 5 1 , − 4 7 , , − 1 9 ) .

Q23:

Find the sum of the last third of the terms in the sequence − 7 8 , − 8 6 , − 9 4 , … , − 1 9 0 .

Q24:

Find the smallest sum for the arithmetic sequence − 1 0 6 , − 9 9 , − 9 2 , … .

Q25:

Find the smallest sum for the arithmetic sequence − 1 0 5 , − 1 0 4 , − 1 0 3 , … .

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